Problem: Rewrite as a simplified fraction. ${3.7\overline{60} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3760.606...\\ 10x &= 37.606...\end{align*}}$ Subtracting the two equations, we have: ${990x = 3723}$ ${x = \dfrac{3723}{990}} $ ${x = \dfrac{1241}{330}} \text{or} {3 \dfrac{251}{330}}$